Multidimensional Signal Restoration and Band-Limited Extrapolation. II.

摘要

This technical report consists of three parts. The central problem is the extrapolation of band-limited signals. In part I, several existing algorithms for band-limited extrapolation are compared: Two-step procedures appeared to give better reconstructions and require less computing time than iterative algorithms. In part II, five basic procedures for iterative restoration are unified using a Hilbert Space approach. In particular, all known interative algorithms for extrapolation of band-limited signals are shown to be special cases of Bialy's iteration. The authors also obtained faster algorithms than that of Papoulis-Gerchberg. In part III, the extrapolation problem is presented in a more general setting: Continuation of certain analytic functions. Presented are two steps procedures for finding the continuation of these functions. Some new procedures for band-limited continuation are also discussed as well as the case in which the signal is contaminated with noise.